Visible crew/equipment: In the scene where Layla drives her VW through the gate you can see a camera lens (a bright circle) in the passenger seat of Clayton's truck. This is the angle used for a brief moment from his view when she crashes through the gate. (01:32:20)
Visible crew/equipment: When James gets into Layla's car after forcing it off the road, the boom mic can be seen in the rear side window of Layla's Volkswagen Beetle.
Suggested correction: A good number of mice and keyboards connect to the computers through the USB ports. If they took out all but two ports, and left those for the mouse and keyboard, it could be possible. If Leila pulled out the keyboard plug she could put in the USB device and copy the files. Heck, she could have even opened the computer up herself and installed a hidden USB drive (smuggling in the tools with her coffee mug of course). She would just have to be sneaky about it, and that's nothing unusual for these characters.
Not only is the original "Corrected entry" valid, it's understated. Burke actually said "Langley's computers don't have disk drives" - not just no floppy drive. In a high-security environment, such a system would be configured so that no USB port could communicate with an external drive; even more likely, the workstations would be dumb terminals - just keyboard, mouse, and monitor; and that's exactly what they appear to be in Layla's office area. So, showing a USB port built into Layla's keyboard and communicating with a USB drive belies a major part of Burke's story, and if Layla were able to do that, the system would immediately "see" it. It's the ersatz "Correction" that's mistaken, since it describes only ordinary commercial computer systems.